Flumini, Dandolo; Sato, Kentaro (2014). From hierarchies to well-foundedness. Archive for mathematical logic, 53(7-8), pp. 855-863. Springer International 10.1007/s00153-014-0392-9
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We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies (of various complexity) have been extensively studied, we point out that (if parameters are allowed) well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting (Π01−CA0)α⊢wf(α)where(Π01−CA0)α stands for the iteration of Π01 comprehension (with parameters) along some ordinal α and wf(α) stands for the well-foundedness of α.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Institute of Computer Science (INF) > Logic and Theory Group (LTG) 08 Faculty of Science > Institute of Computer Science (INF) |
UniBE Contributor: |
Flumini, Dandolo, Sato, Kentaro |
Subjects: |
000 Computer science, knowledge & systems 500 Science > 510 Mathematics |
ISSN: |
0933-5846 |
Publisher: |
Springer International |
Language: |
English |
Submitter: |
Florian Ranzi |
Date Deposited: |
23 Jan 2015 14:50 |
Last Modified: |
05 Dec 2022 14:39 |
Publisher DOI: |
10.1007/s00153-014-0392-9 |
BORIS DOI: |
10.7892/boris.61787 |
URI: |
https://boris.unibe.ch/id/eprint/61787 |
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